SOLUTION: I'm taking algebra and our final project is about how math is related to a Graphic Designer. My scenario is creating a logo. And my logo got chosen. It must now be enlarged for a b

Question 724109: I'm taking algebra and our final project is about how math is related to a Graphic Designer. My scenario is creating a logo. And my logo got chosen. It must now be enlarged for a billboard. Typical billboards are 14 by 48 feet; 12 by 24 feet; and 5 by 11 feet. The largest sign is the one you most often notice along the freeway.
What will the new scale factor need to be? (Hint: Your original design and enlargement were measured in centimeters. Billboards are measured in feet. 1 inch = 2.52 centimeters.)
I haven't made up any dimensions yet. I don't know what a typical logo design size is. Maybe 10cm by 20cm?
How should I solve this? Please help!
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
1 inch=2.54 cm (centimeters) (It's not 2.52).
Your logo (a design drawn on a piece of paper) has been chosen and its measurements (in cm) must be used in the calculations.
(Nowadays, they probably move from rough paper sketches to computer design, and measure sizes in pixels, but let's pretend we draw on paper and use calculators).

Let's say an enlarged logo design is presented on an 8.5" by 11" piece of paper, looking like this:
The logo fits in the green rectangle (touches each of the edges at some point).
The green rectangle is cm wide and cm tall.
On the billboard it will be scaled up by a factor to be cm wide and cm tall.

Let's say that you want to put that logo on a billboard that is tall and wide. That is
wide and
tall.
Do you want to leave some space around the edges of the billboard?
Or would it be OK to make your logo tall?
Let's say it is OK if on the billboard the logo is tall, and it would also be OK if it is wide.
Obviously, you cannot make it larger, because you would have to leave pieces of the logo out of the billboard.
So, the limits for the size of the logo (in cm) are:
-->
and -->
You take the samllest of and as your maximum scale factor.
Once you find and in centimeters (the size of your paper logo), you can find the maximum values of the scale factor to make sure your
logo is not too wide or too tall for the billboard.

IF I had a logo that fits in a rectangle 18cm wide and 15cm tall, I would calculate
to make sure it's not too wide
and to make sure it's not too tall.
So I may decide to use a scale factor of 24.384 to make the logo as tall as the billboard. It will not be as wide as the billboard, but I will figure out what to do with the part of the billboard that is not filled up with the logo. Maybe I'll fit the logo into one side of the billboard and use the rest for some short message in text like "Best in the state." Or maybe I'll center the logo and just add background on both sides.
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